Related papers: Emerging spectra of singular correlation matrices …
Banded random matrices were introduced as a more realistic alternative to full random matrices for describing the spectral statistics of heavy nuclei. Initially considered by Wigner, they have since become a paradigmatic model for…
Complex networks represent system dynamics through the interactions of a set of anomalous time series. Consider the problem of computing correlations for highly correlated pairs of time series across sliding windows. Efficiently computing…
Auxiliary data sources have become increasingly important in epidemiological surveillance, as they are often available at a finer spatial and temporal resolution, larger coverage, and lower latency than traditional surveillance signals. We…
Estimating time-varying correlation matrices is challenging because existing methods may adapt slowly to structural changes, impose insufficient regularization, or produce diffuse posterior uncertainty. In moderate dimensions, an additional…
We demonstrate that extremely rapid and weak periodic and non-periodic signals can easily be detected by using the autocorrelation of intensity as a function of time. We use standard radio-astronomical observations that have artificial…
In this brief review, we critically examine the recent work done on correlation-based networks in financial systems. The structure of empirical correlation matrices constructed from the financial market data changes as the individual stock…
Singular Spectrum Analysis and many other subspace-based methods of signal processing are implicitly relying on the assumption of close proximity of unperturbed and perturbed signal subspaces extracted by the Singular Value Decomposition of…
Understanding the limiting behavior of eigenvalues of random matrices is the central problem of random matrix theory. Classical limit results are known for many models, and there has been significant recent progress in obtaining more…
Random matrix theory allows one to deduce the eigenvalue spectrum of a large matrix given only statistical information about its elements. Such results provide insight into what factors contribute to the stability of complex dynamical…
Recent studies have shown great promise in applying graph neural networks for multivariate time series forecasting, where the interactions of time series are described as a graph structure and the variables are represented as the graph…
This paper proposes a flexible framework for inferring large-scale time-varying and time-lagged correlation networks from multivariate or high-dimensional non-stationary time series with piecewise smooth trends. Built on a novel and unified…
We introduce a method for describing eigenvalue distributions of correlation matrices from multidimensional time series. Using our newly developed matrix H theory, we improve the description of eigenvalue spectra for empirical correlation…
Time series measured from real-world systems are generally noisy, complex and display statistical properties that evolve continuously over time. Here, we present a method that combines wavelet analysis and non-stationary surrogates to…
Random matrix theory is finding an increasing number of applications in the context of information theory and communication systems, especially in studying the properties of complex networks. Such properties include short-term and long-term…
Matrix factorization is a powerful data analysis tool. It has been used in multivariate time series analysis, leading to the decomposition of the series in a small set of latent factors. However, little is known on the statistical…
We discuss a weighted estimation of correlation and covariance matrices from historical financial data. To this end, we introduce a weighting scheme that accounts for similarity of previous market conditions to the present one. The…
In complex systems, crucial parameters are often subject to unpredictable changes in time. Climate, biological evolution and networks provide numerous examples for such non-stationarities. In many cases, improved statistical models are…
A recently developed wavelet based approach is employed to characterize the scaling behavior of spectral fluctuations of random matrix ensembles, as well as complex atomic systems. Our study clearly reveals anti-persistent behavior and…
Correlation matrices are widely used to analyze the interdependence of variables in various real-world scenarios. Often, a perturbation in a few variables leads to mild differences in many correlation coefficients associated with these…
We introduce a new coupled map lattice model in which the weak interaction takes place via rare "collisions". By "collision" we mean a strong (possibly discontinuous) change in the system. For such models we prove uniqueness of the SRB…